With the national presidential polls suddenly looking very tight, here are three ways of looking at the state of the election.

1. An election is like a race. As in a race, the contenders stand in some relation to each other at any given moment. They can increase or reduce their speeds, but it’s an advantage to be in front, and more so as time passes. If an election is like a race, then it becomes increasingly important who’s ahead as the finish line approaches. A race course may have features that favor one or the other contender at a given moment. For instance, each presidential candidate gets a burst of speed after her or his convention, and a debate offers a chance for one of them to speed up or stumble, but the last stretch will be pretty level and even. In that case, it is bad news for Clinton that her lead had dissipated as we’ve moved through September. Much depends on whether that trend continues or reverses in the next few weeks, because by mid-October, a candidate who trails has little time to make up the gap. (That conclusion follows from the race metaphor.) It supports the idea that Trump has as much as a 40% chance of winning.
2. An election is an event that occurs at one moment (although kind of a stretched-out moment nowadays, thanks to early voting). Polls ask people how they will vote once the big moment comes. It’s not clear when our predictions are most accurate, and accuracy may not necessarily increase over time. Instead, we might think of each of the many hundreds of polls taken so far as a measure of how the public will vote once the actual election comes. The best estimate, from this Bayesian perspective, averages all the polls taken so far. It does so not only to maximize the sample size but also to negate the random variations in competitors’ standing due to recent events. As Sam Wang says, “I still expect Clinton’s lead to increase again, on the grounds that she has led all year. Previously, I noted that the national Clinton-vs.-Trump margin in 2016 has averaged 4.5 percentage points. The standard deviation is 2.2 points, comparable to the four Presidential elections from 2004 to 2012. … Today, conditions seem right for regression to the mean.'” There is no such thing as regression to the mean in a race, where the leader accumulates an increasing chance of winning. But this second way of thinking about the election avoids the race analogy. Wang‘s own Bayesian prediction is a little more complicated, but it gives Trump only a 14% chance of winning.
3. An election is an event that will happen at one moment in the future, and each poll is a prediction of what will happen when that moment comes–but the sample that responds to pollsters varies depending on recent events. Democrats, for instance, may have become marginally less likely to answer surveys in the last two weeks because of some generalized discouragement–or Republicans who were going to vote for Trump all along may have become more willing to answer the pollsters’ calls. If this theory applies, I think we should act as Wang recommends, because we should treat the variations in response rates as pretty random. But we might view the real vote as similar to a single poll and ask whether the experience of actually voting will encourage or discourage the people who have been favorable to Clinton or to Trump all along. We cannot tell the answer to that question from poll data, but we might propose reasonable hypotheses about it.

Since I don’t know which of these theories is true, I’m inclined to estimate the odds of a Clinton win somewhere between the Bayesian estimate (86% or so) and the horse race estimate of only about 60%.